If the "jack" is on the top surface of the metal chassis, it's probably the bias adjustment. Look inside the jack and if you see a slot for a screwdriver it's the bias adjustment for the output tubes. It's actually a potentiometer underneath, but it looks like a 1/4" phone jack on the outside. I suspect the GT-H4 may be a sticker from a Groove Tubes output tube that somebody placed there (just a guess). Doesn't sound like anything I've seen on any other Sunn amp.
Ryan